Emphasizing this response. Bayesian models can always produce simple probabilities if you ask them to. E.g., given this data, what is the probability that the next flip is heads?
The fact that the model is represented as a distribution over Bernoulli parameter p doesn't contradict this: you just integrate over the posterior.
The fact that the model is represented as a distribution over Bernoulli parameter p doesn't contradict this: you just integrate over the posterior.